Isothermal* and Adiabatics.
be actually measured (see Fig. 325); but as these curves have
definite formulae, it is easier to use algebraic methods. Then,
y
Area of curve having formula PV = C is PV x loge ,
vi
and as PV = cr. and = the ratio of expansion r.
v,
Area = cr loge r. (Seep. 1131.)
(Use hyperbolic logarithms, and see Fig. 612)
Area of curve having formula PVW = C is ------??
71 I
Isothermals and Adiabatics.If a gas expand, and
advance a piston against a resistance, it does work requiring
expenditure of heat. Such heat being abstracted from the gas,
the temperature of the latter falls; but if heat be supplied just
as fast as it is abstracted, viz. equal to the work done, the tem-
perature will remain constant, the expansion be according to
Boyle (PV =» C), and the curve be called an isothermal.
If no heat be supplied, the pressure-volume curve will fall
below the hyperbola, as in Fig. 613, according to the formula
PV" = C, and be then termed an adiatiatic. Similarly, in com-
pressing, the adiabatic will rise above the isothermal, because
the gas becomes t heated by work done upon it (Fig. 614).
(See Appendix IL,p. 879.)
Adiabatic Exponent.The value of n will now be found
for the adiabatic.
Area of curve
n _
('I-'
External work,
Total work = Internal work + External work
- <- - '-> -->_+,K-K') - h - o (SSf
* Notice change of sign in two places in order to balance.